Manifestation of the Penning effect in gas proportional counters

Nuclear Instruments and Methods in Physics Research A 735 (2014) 528–531

Contents lists available at ScienceDirect

Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Manifestation of the Penning effect in gas proportional counters Tadeusz Kowalski n AGH, University of Science and Technology, Al. Mickiewicza 30, 30-057 Krakow, Poland

art ic l e i nf o

a b s t r a c t

Article history: Received 13 April 2013 Received in revised form 30 August 2013 Accepted 2 September 2013 Available online 27 September 2013

Penning transfer has significant influence on electron avalanche growth in mixtures in which the ionization potential of quenching agent is below excitation levels of the main gas. The influence of the Penning effect on gas gain factor, effective ionisation potential and on ɑ/p as the function of admixture concentration (from spectroscopically pure main gas up to few percentage of admixture) is shown for Ar and Kr based working gas with cyclohexane, ethanol, isopentane and CO2 as the quenchers. & 2013 Elsevier B.V. All rights reserved.

Keywords: Gas detector Gas gain Penning effect

becomes the major process

1. Introduction Electron traversing the gas or the mixture of gases and vapours in presence of electrical field reaches threshold energy for different interaction processes. Apart from the Townsend ionization mechanism: e þM-e þ e þM þ ;

ð1Þ

e þB-eþ e þ B þ ;

ð2Þ

where M ðBÞ and M þ ðB þ Þ are the atoms and the ions of the main gas (quenching admixture), respectively, a number of phenomena take place which can significantly change the growth of the electron avalanche. Among them there are the excitations of the atoms of the main gas to metastable levels Mm , or to resonance levels Mn . e þM-e þ Mm ;

ð3Þ

e þM-e þ M

ð4Þ

The generated low density plasma contains electrons and ions, as well as atoms excited to metastable or resonance states. In pure gases the metastable atoms deexcite mainly in three body collisions to keep the energy and momentum preservation Mm þ M þ M-Mm 2 þ M-M þ M þ M þ hν;

ð5Þ

hν—energy of the emitted photon. Small amount (  100 ppm) of an admixture B, with ionisation potential lower than the energy of metastable states leads to rapid decrease of the probability of process (5). The Penning quenching n

Corresponding author. Tel.: þ 48 12 6173375; fax: þ 48 12 6340010. E-mail address: Tadeusz.Kowalski@fis.agh.edu.pl

0168-9002/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2013.09.022

Mm þ B-M þ B þ þ e

ð6Þ

The main de-excitation processes for atoms excited to resonance states Mn, are: three body collisions [1], transitions to an excited lower level by collision with a ground state atom M [2], radiative transitions to a lower excited level [2], formation of molecular ions through the Hornbeck–Molnar process [3], radiative de-excitation [1]. For the amount of the admixture B on the level of few percent [4,2,5] non-metastable Penning effect is observed Mn þ B-M þB þ þ e

ð7Þ

Processes (6) and (7), leading to production of additional electrons are particularly interesting for the growth of an electron avalanche in the proportional mode. If one wants to calculate the gas gain or develop the model of electron avalanche growth must keep in mind on this possibility of ionising energy transfer. Probability of processes (6) and (7) is just a balance between transfer reaction and non-ionizing decay of excited states [6]. In this paper, the manifestation, appearance of metastable and non-metastable Penning effect is shown for Ar and Kr based mixtures with cyclohexane, isopentane, ethanol and CO2 as the admixtures. The admixtures were selected to have proper value of ionisation potential compare to excitation levels, see Table 1.

2. Manifestation of Penning effect in gas gain curves Gas amplification factors over the range from 1 to 8  103 were measured for Arþisopentane mixtures ranging from spectroscopically pure Ar up to 5.0% isopentane as a function of the applied voltage between cathode and anode, for mixture pressure 880 hPa.

T. Kowalski / Nuclear Instruments and Methods in Physics Research A 735 (2014) 528–531

Table 1 The values of the energy of excited states of Ar and Kr and the ionization potentials of the used admixtures [5,6,15,16]. Gaz

Metastable levels [eV]

Resonanse levels [eV]

Resonanse 3D levels [eV]

Used ionization potential [eV]

Ar

11.55 11.72 9.915 10.56

11.62 11.83 10.03 10.64

14.09 14.26

15.76

Kr Isopentane Cycloheksane Ethanol CO2

13.996 10.45 10.3 10.6 13.79

529

3. Manifestation of the Penning effect in concentration dependence on effective ionization potential Any theory of ionization in an electrical field attempts to derive a relation between the first Townsend coefficient α, i.e. the number of the electron-ions pairs produced when an electron has moved one unit length in the direction of electrical field, and the state of the gas, its molecular properties and reduced electrical field strength. Aoyama [7] proposed and obtained that: α ¼ K  Sm  expð  L=S1  m Þ; 0 r m r 1 ð8Þ p and derived for gas gain A ln A 1 1 1  ¼  exp  ð L  Sm Þ; a p r a Sa 1  m vi

ð9Þ

where K, L and m—characteristic constants for the gas mixture, Sa —reduced electrical field strength on anode surface and V i —effective ionization potential, p—working gas pressure. The V i was defined as Z r þ λi e E dr þ ε0 ¼ e  V i ; ð10Þ r

Fig. 1. Concentration dependence of gas gain coefficient A, for Ar þisopentane mixtures for fixed applied high voltage. The occurrence of Penning effect is manifested by the wide maximum. Spectroscopically pure Ar is marked as admixture concentration of 10  5.

A cylindrical proportional counter of cathode radius rc ¼14.5 mm with an axially placed anode of radius ra ¼ 50 mm, was used for measurements. The counter was connected to a vacuum system, enabling rapid changes in counter filling. The value of the gas amplification factor was measured using the current method. The gas gain, A, has been determined as the ratio I/Io, where I and Io are the measured current intensities at constant intensity of the incoming photons of X-rays for the applied voltage and for the ionization chamber regime, respectively. To minimize the error in Io and the dark current a special grid of guard rings protecting the anode has been constructed. Apart of this, the dark current was also measured. Current measurements were made in the range 10  12–8  10  10 A, at decreasing radiation intensities, for different values of applied voltage, in the range 50–2300 V. 55Fe radioisotope, of 5.9 keV was used as the radiation source. The accuracy of measurement of the gas amplification factor is limited by the error of measuring the current I0 in the ionization chamber regime, and of measuring the current intensity, I, for different voltages (ΔI0/I0  2.5% and ΔI/I  2%). The concentration dependence of the gas gain coefficient, A(c), for a fixed high voltage is presented in Fig. 1 where a wide maximum at concentrations 10  4– 10  2 is seen. This maximum is due to increase of the first Townsend ionization coefficient α induced by the generation of additional electrons by the Penning effect in the electron avalanche multiplication region. For admixture concentration cr5  10  3 the increase of the gas gain is due to increase of the probability of process (6). On the other hand, the increase of c cools the electrons. The overlapping of these two processes gives the wide maximum of A, for fixed anode– cathode voltages.

where r—any point in the counter, λi —the mean path length for an electron to travel in the field direction to ionize a gas molecule, ε0 —initial electron energy, energy which electron has immediately after the scattering by a gas molecule averaged in the field direction, e—elementary charge and E—electrical field strength. The left side of Eq. (10) is just the sum of the energy that an electron gained from the electric field and, ε0 , so eV i is just the energy of electron just before next ionizing interaction. 1 Eq. (9) can be reduced to the linear relation between Sm and a ln [lnA/(praSa)]   ln A 1 ln ¼ L  Sm – ln M; ðM ¼ ð1–mÞ  V i Þ ð11Þ a pr a Sa This formula in reality contains three unknown parameters L, M and m. For the measured, experimental data of gas gain, A, using the method of least square, for m varying from 0.05 to 0.95 in step of 0.01, the values of L and M were calculated. On the base of correlation coefficient the best fit was selected, thus giving the proper value of L, M and m. It should be underline that mostly the correlation coefficient was of the order of 0.9998. As M¼ (1  m) V i , the value of V i was recalculated. Values of V i for Kr þcyclohexane, Kr þethanol and Kr þ isopentane as function of admixture concentration are shown in Figs. 2–4. The value of V i for spectroscopically pure Kr is shown as for 3×10  5 concentration. A wide minimum in V i (c) dependence (Figs. 2 and 3) for concentration from 310  5 to 6  10  3 is due to process (6) and much smaller but clearly seen (Figs. 2–4) for admixture concentration cr  (2–3)% is due to process (7). Taking into account that for E/p in the range from 10 to 100 [V m  1 Pa  1], values which we have in our measurements, the ratio of excitation to ionization is  (2–3), [8], for co10  3 and V i below ionization potential of Kr (see Table 1), one can conclude that the growth of electron avalanche is via process (6) not via direct Townsend ionization (processes (1) and (2)).

4. Manifestation of the Penning effect in the α/p concentration dependence Zastawny [10] points out that in counter of cylindrical geometry, the expression Z Sa ln A α dS  2 ¼ FðSa Þ ; ¼ ð12Þ pr a Sa S S0 p

530

T. Kowalski / Nuclear Instruments and Methods in Physics Research A 735 (2014) 528–531

is unique function of reduced electrical field strength at the anode surface Sa. S0 is the value of S at the starting point of the avalanche ionization. Using appropriate analytical function for α/p, one can get the function for F(Sa). According to the assumed formula for α/p and obtained function for F(Sa), diagram should be linear. Having experimentally determined function F(Sa), α/p can be calculated. Since several different formulae are used in literature for the first Townsend ionization coefficient, for the description of gas amplification in proportional counters, Zastawny [10] proposed that the original, semi-empirical formula of Townsend should be used as a standard one, Eq. (13), α ¼ C 1  e  C 2 =S ð13Þ p The gas amplification coefficient is expressed as [11], ln A C1 ¼ FðSa Þ ¼  e  C 2 =Sa p r a Sa C2

ð14Þ

Fig. 2. Concentration dependence of Vi for Krþ cyclohexane mixtures. Concentration 10  5 means spectroscopically pure Kr. Concentration, cr (near 1–3%), for which Vi reach minimum is proportional to cr  1/p. This implies that the life time of the resonance states does not depend on p for the studied range of pressures. This result is in agreement with ref. [9] but in disagreement with Ref. [1]. Vi E0 (c¼4.8  10  4) means that there is no direct ionization, electron multiplication is only via the Penning effect.

Fig. 5. Gas gain given as ln[lnA/(p  ra  Sa)] vs. Sa  1, for Arþ CO2 mixtures. In this coordinates the diagram should be linear.

Fig. 3. Effective ionization potential Vi, as function of ethanol concentration in Kr.

Fig. 4. Effective ionization potential Vi, as function of isopentane concentration. Have a look on the change in minimum position for different mixture pressures.

Fig. 6. Dependence of α/p on CO2 concentration in Ar. Reduced electrical field strength on anode surface Sa, is the curves parameter.

T. Kowalski / Nuclear Instruments and Methods in Physics Research A 735 (2014) 528–531

531

Fig. 7. Scheme of gas system for mixture preparation and read out electronic. Cylinders with Ar and CO2 on the left. HT—HI-TEC, mass flow meters and controllers; PC— proportional counter; PA—preamplifier, ORTEC Model 142 PC; A—amplifier, ORTEC Model 575 A; MCA—Multichannel analyzer, ORTEC Triumph PC; CM—concentration monitor, SERVOMEX, 1440 gas analyzer; HV—high voltage power supply, CAEN Model 472; PT—pressure transducer, SETRA systems.

in Fig. 6 as the function of CO2 concentration for fixed reduced electrical field. Peak in α/p is observed for CO2 concentration near 20% for high value of reduced field strength, higher than 80 [V m  1 Pa  1]. For low value of Sa, slight decrease in α/p with CO2 concentration is observed. This is the consequence of lowering electron energy in non-elastical scattering with CO2. The increase in the α/p can be explained by the Penning effect [14]. The excited Ar atoms to 3D levels (for details see Table 1) in the reaction, Eq. (7) provide to production of additional electrons. In current measurements of gas gain the CO2 concentration was changed in the step of 5% or 10%. To localize more precisely the concentration for which α/p has the maximum additional measurements were performed. Using the set shown in Fig. 7 the peak position of 55Fe —line was measured for CO2 insertion from 18% to 27% in step of  1% (see Fig. 8). It is typical dependence, but in Fig. 9 the slope of this curve is shown. There is clearly seen change in the slope for c  24%. It is the evidence of the Penning effect on 3D—Ar states [13]. Fig. 8. Peak position of

55

Fe-line as the function of admixture concentration.

5. Conclusions Results presented here are based on the measurements of 77 standard gas gain curves, i.e. gas gain factor as the function of applied voltage. Measurements were made for Ar and Kr as the main gas with admixture of isopentane, cyclohexane, methanol and CO2 over wide range of concentration, from spectroscopically pure noble gases up to few percentage of additives mainly for atmospheric pressure. Some limited number of measurements was done also for lower pressure. The composition of mixtures were specially selected to show the occurring of Penning process, i.e. the ionization potential of additives was below the excited states of Ar or Kr. The Penning transfer in all studied mixtures is clearly seen.

References

Fig. 9. Slope of the curve, Fig. 8. Change in the slope for c  24% is clearly seen. Similar results were also obtained for U¼ 1500 V.

The constants C1 and C2 are determined from the measurements of the gas amplification factor, A. To calculate α/p [12,13] from the above formula, the relationships ln[lnA/(praSa)] versus Sa  1 are shown for all measured CO2 concentration in Fig. 5. The choice of coordinates is such that experimental points should be on straight line. The constants C1 and C2 are just straight line parameters. Using the formula (13) and experimentally determined constants, C1 and C2, α/p has been calculated and displayed

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]

N. Thonnard, G.S. Hurst, Physical Review A5 (1972) 1110. S. Kubota, Journal of the Physical Society of Japan 29 (1970) 1017. J.A. Hornbech, J.P. Molnar, Physical Review 84 (1951) 621. T.Z. Kowalski, J. Zając, Nuclear Instruments and Methods A 249 (1986) 426. ICRU Report No 31, 1979. Ö. Sahin et al., 2010 JINST 5 P05002. T. Aoyama, Nuclear Instruments and Methods A 234 (1985) 125. A.A. Kruithof, Physica VII 6 (1940) 519. T. Holstein, Physical Review 83 (1951) 1159. A. Zastawny, Nuclear Instruments and Methods A 385 (1997) 239. A. Williams, R.I. Sara, International Journal of Applied Radiation and Isotopes 13 (1962) 229. Yu.I. Davydow, IEEE Transactions on Nuclear Science NS53 (5) (2006) )2931. G. Auriemma, et al., Nuclear Instruments and Methods A 513 (2003) 484. A. Andronic, et al., Nuclear Instruments and Methods A 523 (2004) 302. R.I. Reed, Ion Production by Electron Impact, Academic Press, London and New York, 1962.